Tube Wave Attenuation and In-Situ Permeability

Abstract

The measurement of in-situ permeability is very important in exploration and production logging. Observed data show that tube wave attenuation in full waveform acoustic logs is correlated with formation permeability. It is postulated that attenuation is due to fluid flowing away from the borehole into the formation. In this paper we investigate the theoretical relationship between tube wave attenuation and permeability using two different models. The first is a simple model of a borehole with absorbing walls, and the second is a borehole with a Biot porous medium in the formation. Both models give qualitatively similar results. Tube wave attenuation increases with increasing permeability. Attenuation also increases with increasing frequency and porosity. We have also investigated the relative effects of intrinsic formation attenuation (anelasticity) and permeability on the attenuation of tube waves. Intrinsic attenuation was introduced into the models by means of complex velocities. It is found that in rocks with low to medium permeability (less than 100 millidarcies), intrinsic attenuation is the major contributor to tube wave attenuation. However, in high permeability (greater than 100 millidarcies) rocks, fluid flow associated with in-situ permeability is as important as intrinsic attenuation in controlling tube wave attenuation. In either case, if one can estimate the intrinsic formation attenuation from the other parts of the full waveform (such as the P wave or the psuedo-Rayleigh wave), an estimate of the permeability of the formation can be obtained. We tested the models using published data on core permeability and tube wave amplitudes. By assuming an average value of intrinsic attenuation appropriate to the formations under study, we obtained a good agreement between theory and data.